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The integral int(sec^2x)/((secx+tanx)^(9...

The integral `int(sec^2x)/((secx+tanx)^(9//2))dx ` equals for some arbitrary constant k

A

`(-1)/((sec x + tan x)^(11//2)){1/11-1/7(sec x+tanx)^2]+k`

B

`(1)/((sec x + tan x)^(11//2)){1/11-1/7(sec x+tanx)^2]+k`

C

`(-1)/((sec x + tan x)^(11//2)){1/11+1/7(sec x+tanx)^2]+k`

D

`(1)/((sec x + tan x)^(11//2)){1/11+1/7(sec x+tanx)^2]+k`

Text Solution

Verified by Experts

The correct Answer is:
C
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The integral int (sec^2x)/(secx+tanx)^(9/2)dx equals to (for some arbitrary constant K ) (A) -1/(secx+tanx)^(11/2){1/11-1/7(secx+tanx)^2}+K (B) 1/(secx+tanx)^(11/2){1/11-1/7(secx+tanx)^2}+K (C) -1/(secx+tanx)^(11/2){1/11+1/7(secx+tanx)^2}+K (D) 1/(secx+tanx)^(11/2){1/11+1/7(secx+tanx)^2}+K

The integral int(sec^(2)x)/((sec x+tan x)^((9)/(2)))dx equals (for some arbitrary constant K)-(1)/((sec x+tan x)^((11)/(2))){(1)/(11)-(1)/(7)(sec x+tan x)^(2)}+K(1)/((sec x+tan x)^((11)/(2))){(1)/(11)-(1)/(7)(sec x+tan x)^(2)}+K-(1)/((sec x+tan x)^((11)/(2))){(1)/(11)+(1)/(7)(sec x+tan x)^(2)}+K

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